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Solved Examples
Lesson 75 of 117 • 2 upvotes • 6:12mins
Asim Anand
Solved Examples
Mathematics Optional for UPSC - ODE And PDE
117 lessons • 13h 32m
1
Overview
1:43mins
2
Formulation of Differential Equations - I
10:57mins
3
Formulation of Differential Equations - II
11:48mins
4
Formulation of Differential Equations - III
10:21mins
5
Formulation of Differential Equations - IV
9:15mins
6
Solved Examples - I
13:08mins
7
Solved Examples - II
6:33mins
8
Equations of First Order and First Degree - I
10:14mins
9
Equations of First Order and First Degree - II
10:07mins
10
Equations of First Order and First Degree - III
10:44mins
11
Equations of First Order and First Degree - IV
8:39mins
12
Please omit this lesson.
1:37mins
13
Equations of First Order and First Degree - V
13:04mins
14
Equations of First Order and First Degree - VI
11:40mins
15
Equations of First Order and First Degree - VII
12:25mins
16
Equations of First Order and First Degree - VIII
8:53mins
17
Solved Examples - I
11:48mins
18
Solved Examples - II
14:30mins
19
Solved Examples - III
11:26mins
20
Solved Examples - IV
14:30mins
21
Solved Examples - V
14:16mins
22
Solved Examples - VI
14:52mins
23
Solved Examples - VII
4:36mins
24
Trajectories - I
12:27mins
25
Trajectories - II
12:11mins
26
Trajectories - III
7:38mins
27
Equations of First Order but not of First Degree - I
8:53mins
28
Equations of First Order but not of First Degree - II
12:47mins
29
Equations of First Order but not of First Degree - III
11:10mins
30
Clairaut's Equation
3:38mins
31
Equations reducible to the Clairaut's Form
8:14mins
32
Singular Solutions - Introduction
10:15mins
33
C - discriminant and p - discriminant Relations
4:54mins
34
Determination of Singular Solutions
6:34mins
35
Working rule - Method I
3:07mins
36
Working rule - Method II
1:19mins
38
Singular Solution of Clairaut's Equation
2:18mins
39
Solved Examples
13:20mins
40
Linear Differential Equations with Constant Coefficients - Notations
7:16mins
41
Linear Differential Equations with Constant Coefficients - Introduction
7:59mins
42
Linear Differential Equations with Constant Coefficients - Complementary Function (C.F.)
7:03mins
43
Auxiliary Equation - Case of Real & Distinct roots
1:05mins
44
Auxiliary Equation - Case of Equal roots
4:35mins
45
Auxiliary Equation - Case of Complex Roots
2:52mins
46
Auxiliary Equation - Case of Surd Roots
3:58mins
47
Complementary Function - Working Rule & Summary
4:36mins
48
Solved Examples
5:12mins
49
The Symbolic Function 1/f(D)
2:08mins
50
Linear Differential Equations with Constant Coefficients - Particular Integral (P.I.)
7:23mins
51
Particular Integral - Working Rule
2:15mins
52
Solved Example
3:42mins
53
Particular Integral - Short Method I
9:30mins
54
Solved Examples
5:41mins
55
Particular Integral - Short Method II
12:51mins
56
Solved Examples
2:45mins
57
Particular Integral - Short Method III
3:56mins
58
Solved Examples
7:30mins
59
Particular Integral - Short Method IV
4:08mins
60
Solved Examples
4:38mins
61
Particular Integral - Short Method V
9:09mins
62
Solved Examples
5:25mins
63
Method of Undetermined Coefficients
6:45mins
64
Method of Undetermined Coefficients - Modifications to the Trial solution
9:06mins
65
Solved Examples
5:01mins
66
Cauchy-Euler Equations - Introduction
1:51mins
67
Cauchy-Euler Equations - Method of solution
5:21mins
68
Solved Examples
4:37mins
69
Cauchy-Euler Equations - Particular Integral
4:52mins
70
Particular cases
5:07mins
71
Solved Examples
8:31mins
72
Legendre's Linear Equation - Introduction
1:17mins
73
Legendre's Linear Equations - Method of Solution
4:32mins
74
Legendre's Linear Equation - Working Rule
2:06mins
75
Solved Examples
6:12mins
76
Method of Variation of Parameters - First Order Equations
4:51mins
77
Working Rule & Illustrative Example
4:14mins
78
Method of Variation of Parameters - Second Order Equations
6:58mins
79
Working Rule
2:37mins
80
Solved Example
3:22mins
81
Simultaneous Differential Equations - Introduction
2:39mins
82
Simultaneous Differential Equations - Method I & Example
7:46mins
83
Simultaneous Differential Equations - Method II & Example
4:53mins
84
Solved Examples
9:13mins
85
Simultaneous Differential Equations involving x•d/dx or t•d/dt
3:04mins
86
Exact Differential Equation - Introduction
2:04mins
87
Condition of Exactness
10:42mins
88
Solved Examples
9:36mins
89
Integrating Factor
1:06mins
90
Solved Example
4:23mins
91
Exactness of Non-Linear Equations - I
10:52mins
92
Exactness of Non-Linear Equations - II
3:42mins
93
Equations of the form (d^n y/dx^n) = f(x)
2:55mins
94
Equations of the form (d^2 y/dx^2) = f(y)
5:08mins
95
Reduction of Order - Equations that don't contain y directly
3:41mins
96
Equations that don't contain x directly
6:05mins
97
Linear Equations of Second Order - Motivation
0:42mins
98
Complete Solution of y'' + Py' + Qy = R in terms of one known Integral
7:03mins
99
Rules for getting an Integral belonging to C.F.
3:39mins
100
Working Rule
2:15mins
101
Theorem
7:22mins
102
Solved Examples
7:09mins
103
Reduction to Normal Form
4:38mins
104
Working Rule & Trick to Remember
4:02mins
105
Solved Examples
4:03mins
106
Transformation of Equation - Changing the Independent variable
4:01mins
107
Working Rule
3:48mins
108
Solved Examples
6:43mins
109
Theorem
2:40mins
110
Solutions by Operators
1:53mins
111
Solved Example & Concluding Note (ODE)
4:47mins
112
CSE Mains 2018 Solutions (ODE)
11:55mins
113
CSE Mains 2017 Solutions (ODE)
12:36mins
114
CSE Mains 2016 Solutions (ODE)
13:55mins
115
CSE Mains 2015 Solutions (ODE)
14:20mins
116
CSE Mains 2014 Solutions (ODE)
14:44mins
117
CSE Mains 2013 Solutions (ODE)
10:57mins
118
CSE Mains 2012 Solutions (ODE)
11:38mins
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